Think that all the best inventions happen in rich countries and trickle down to poor ones? Think again.

Here’s the story we’ve been hearing for years: Back in 1965 the coach of the University of Florida football team was befuddled that no matter how much water his players drank, they still became badly dehydrated in the brutal Florida heat and humidity. He asked doctors at the college for advice and one of them, James Robert Cade, devised a concoction of sucrose, glucose, sodium and potassium. Unfortunately, it tasted worse than a bucket of sweat. Cade’s wife suggested adding lemon juice and soon the world would be gulping Gatorade.

The part of the tale we never hear is that Cade got the idea from reading about doctors who went to Bangladesh during a cholera outbreak. They discovered that the locals were using a drink made of carrot juice, rice water, bananas, and carob flour–a combo of carbs and sugar–to rehydrate those suffering severe diarrhea.

This is what’s become known as “reverse innovation”–ideas that move from poor to rich nations. It’s just one of several examples that Dartmouth professors Vijay Govindarajan and Chris Trimble roll out in their new book, Reverse Innovation: Create Far From Home, Win Everywhere. As Govindarajan learned while working as an “innovation consultant” for General Electric (GE), the notion that all the good ideas come from developed countries and simply are tweaked to work in more primitive places is an increasingly flawed concept.

It’s a small world after all

Instead, more and more products, even business strategies, are bubbling up first in “emerging” countries, then flowing uphill into mature markets. Take the case of the GE’s Vscan. It’s an ultrasound scanner not much bigger than a smart phone. But it didn’t start out that way. Not even close. No, GE’s original plan when it moved into the Chinese market was to sell the big, expensive–starting at $100,000–ultrasound machines that you see in so many American hospitals.

Chinese hospitals didn’t have that kind of money. And besides, what was really needed was a portable scanner that a doctor could use on patients in rural areas. So GE started thinking small. And it shifted its focus from high-priced hardware to relatively inexpensive software. This was shrewd. The Vscan has grown from a $4 million to a $278 million business and now American and European hospitals and doctors want them. GE CEO Jeff Immelt has gone so far as to predict that the Vscan could become “the stethoscope of the 21st century.”

Another example: After Wal-Mart discovered that its massive stores didn’t work very well in countries like China, Argentina and Mexico because a lot of shoppers had neither the money nor the storage space to buy in bulk, it scaled way back to models known as “small marts.” It then realized that this approach might work in the U.S., too, in places where buildings the size of airplane hangars didn’t make a lot of sense. So, last year the first of these shrunken stores, called Wal-Mart Express, opened in rural Arkansas. The second and third followed in urban Chicago.

“What works in the rich world won’t automatically achieve wide acceptance in emerging markets, where customer needs are starkly different,” writes Govindarajan. “As a result, reverse innovation is rapidly gathering steam–and will only continue to do so.”

Bright lights, big cities

More evidence of the global shifts of innovation comes from a database released by the Organization for Economic Cooperation and Development. By tracking international patents and patent applications, it found, not surprisingly, that inventions tends to flow out of the world’s cities–93 percent of patent applications are generated by inventors in metro areas accounting for only 23 percent of the planet’s population.

But the stats also show the U.S. losing ground on the innovation front. Its share of global patents fell from 40 percent at the turn of the century to 28 percent by 2010. Meanwhile, China saw its share rise by 6 percent over the same period.

And if all the social interactions and economic diversity that come with city living do help drive innovative thinking, as a lot of research suggests, developing countries would seem to be primed for a century of invention. Of the 25 fastest growing major cities in the world, seven are in China, six are in India. By 2025, only two of the 15 largest mega-cities–New York and Tokyo–will be in what are now developed countries.

Did you feel the Earth tilt?

Meanwhile, On the other side of the planet

Here are examples of innovative projects underway in developing countries:

Don’t look down. No, really: Now this is not for the faint of heart. After five years of construction, a suspension bridge more than 1,100 feet high and more than 3,800 feet long opened recently in China’s Hunan Province. If, God forbid, your car went over the side, it would take eight seconds to hit bottom.

Start me up: India has launched its first telecom “incubator,” a private-public partnership called Startup Village, which hopes to boost 1,000 startups over the next decade. It’s modeled after a Silicon Valley program that helps finance student innovations.

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